Finite Group Databasebeta

← #11792278

Subgroups — #11792278

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10591221C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72110—31nomaximal
9#71881—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#951—22no—
16C3×#951—22no—
17C3×#946—21no—
18C2×C3×#216—21no—
19C3×#939—22no—
20C3×#938—21no—
21C2×C3×#214—21no—
22C3×#930—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924—21no—
25C2×C3×#208C2211yescharacteristic
26C2×#3718—21no—
27#63827—22no—
28#63827—22no—
29C2×#3715—21no—
30#63664—22no—
31#63579—22no—
32#63568—22no—
33C2×C3×#137—31no—
34C3×#537—31no—
35#5833D311yescharacteristic
36C2×#951—31no—
37C2×#951D311yescharacteristic, complemented
38C2×#942—31no—
39C2×#837—31no—
40C2×#837—31no—
41C2×#837—31no—
42C2×#837—61no—
43#5229—31no—
44C2×#825—31no—
45#4973—31no—
46#4554—31no—
47#4530—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×C3×#67—21no—
59C2×C3×#67—22no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic
67C2×C3×C4×D3—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6D412yescomplemented
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3—21no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×#217—22no—
81C3×#216—24no—
82C3×#214—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×Dic3⋊C4—22no—
87C3×#208—21no—
88C3×#208D412yescomplemented
89C2×C3×C3⋊C8—21no—
90#3718—24no—
91#3715—24no—
92#2007—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C2×D311yescharacteristic
97C22×C3×Q8—31no—
98C2×#235C2×D311yescharacteristic
99C22×Dic6C2×D311yescharacteristic
100C3×#137—62no—
101C3×#137—62no—
102C2×C3×Q16—61no—
103C2×C3×SD16—61no—
104C2×C3×M16—31no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—61no—
107C3×#121—61no—
108C3×#121—62no—
109C3×#121—61no—
110C2×C3×C4⋊C4—31no—
111#951—22no—
112#951—22no—
113#951—62no—
114#951—62no—
115#946—21no—
116C2×#216—21no—
117C2×#216—61no—
118C2×#216—61no—
119#942—62no—
120#942—62no—
121C2×#215—61no—
122#939—22no—
123#938—21no—
124C2×#214—21no—
125C2×#214—61no—
126#930—21no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128#924—21no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—61no—
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C2×#208C2×D311yescharacteristic
136#837—62no—
137#837—62no—
138#837—64no—
139#837—62no—
140C3⋊#95—62no—
141C3⋊#95—62no—
142#825—62no—
143C23×C32—21no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—41no—
151C32×D4—41no—
152C2×C32×C4—21no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—41no—
164C3×#67—41no—
165C3×#67—41no—
166C3×#67—82no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—42no—
173C3×D12—21no—
174C3×D12—21no—
175C3×C4×D3—41no—
176C3×C4×D3—41no—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—41no—
182C3×Dic6—41no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185C2×#137—31no—
186C2×#137—91no—
187#537—31no—
188C2×#104—91no—
189C2×#104—91no—
190#391—91no—
191#343—91no—
192C3×#41—22no—
193C3×#41—22no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—21no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—41no—
203C3×#41—41no—
204C3×#41—61no—
205C3×#41—61no—
206C3×#41—61no—
207C3×#41—61no—
208C2×C3×Q8—21no—
209C2×C3×Q8—32no—
210C2×C3×Q8—31no—
211C2×C3×Q8—61no—
212C2×C3×Q8—61no—
213C2×C3×Q8—61no—
214C2×C3×Q8—61no—
215C2×C3×Q8—61no—
216C2×C3×Q8#6711yescharacteristic
217C2×C3×Q8#6711yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—31no—
222C2×C3×D4—41no—
223C2×C3×D4—61no—
224C2×C3×D4—62no—
225C2×C3×D4#6711yescharacteristic
226C2×C3×D4#6711yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—32no—
231C22×C3×C4—41no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—21no—
237C2×#67—22no—
238C22×Dic3—21no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—121no—
242C22×Dic3#6712yes—
243#235—21no—
244#235—21no—
245#235—21no—
246#235—21no—
247C2×D12#6711yescharacteristic
248C2×C4×D3—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6#6711yescharacteristic
255C2×Dic6#6712yescomplemented
256C3×Q16—64no—
257C3×SD16—64no—
258C3×M16—32no—
259C3×M16—61no—
260C2×C3×C8—61no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266#217—22no—
267#216—24no—
268#216—64no—
269#216—64no—
270#215—64no—
271#214—24no—
272#214—64no—
273(C2×D3)⋊C4—22no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276Dic3⋊C4—22no—
277C4×Dic3—62no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—121no—
283#208—21no—
284#208—32no—
285#208—32no—
286#208—62no—
287#208—61no—
288#208—61no—
289#208—121no—
290#208#6712yescomplemented
291C2×C3⋊C8—21no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—121no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32#12011yescharacteristic
301C22×C32#12111yescharacteristic
302C22×C32#12711yescharacteristic
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C32×C4—41no—
307C32×C4#12011yescharacteristic
308C32×C4#12011yescharacteristic
309C32×C4#12111yescharacteristic
310C32×C4#12111yescharacteristic
311C3⋊Dic3—42no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41D3211yescharacteristic
317C22×Q8—31no—
318#137—62no—
319#137—62no—
320#137—182no—
321#137—182no—
322C2×Q16—61no—
323C2×Q16—181no—
324C2×SD16—61no—
325C2×SD16—181no—
326C2×M16—31no—
327C2×M16—91no—
328C22⋊Q8—61no—
329C22⋊Q8—61no—
330#121—61no—
331#121—62no—
332#121—61no—
333C2×C4⋊C4—31no—
334C2×C42—91no—
335#104—182no—
336#104—182no—
337#95—182no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—41no—
342C23×C3—61no—
343C23×C3D3×D411yescharacteristic
344C23×C3C2×#6711yescharacteristic
345C22×D3—21no—
346C3×Q8—22no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—21no—
351C3×Q8—41no—
352C3×Q8—62no—
353C3×Q8—61no—
354C3×Q8—62no—
355C3×Q8—61no—
356C3×Q8—121no—
357C3×Q8—121no—
358C3×D4—22no—
359C3×D4—21no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—41no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—61no—
371C3×D4—61no—
372C3×D4—121no—
373C3×D4—121no—
374C3×D4—242no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—121no—
394C2×C3×C4—121no—
395C2×C3×C4—121no—
396C2×C3×C4—121no—
397C2×C3×C4—122no—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4#23711yescharacteristic
404C2×C3×C4#23711yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410#67—41no—
411#67—41no—
412#67—82no—
413C2×Dic3—22no—
414C2×Dic3—21no—
415C2×Dic3—22no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—42no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—122no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428D12—21no—
429D12—21no—
430C4×D3—41no—
431C4×D3—41no—
432Dic6—22no—
433Dic6—21no—
434Dic6—21no—
435Dic6—22no—
436Dic6—41no—
437Dic6—41no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—62no—
441C3⋊C8—62no—
442C3⋊C8—122no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—81no—
446C2×C32#39211yescharacteristic
447C2×C32#45511yescharacteristic
448C2×C32#45611yescharacteristic
449C3×D3—81no—
450#41—21no—
451#41—21no—
452#41—21no—
453#41—21no—
454#41—61no—
455#41—61no—
456#41—61no—
457#41—61no—
458C2×Q8—31no—
459C2×Q8—32no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×Q8—61no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8#62511yescharacteristic
466C2×D4—21no—
467C2×D4—31no—
468C2×D4—61no—
469C2×D4—62no—
470C2×D4#62511yescharacteristic
471C22×C4—21no—
472C22×C4—32no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477Q16—64no—
478Q16—184no—
479SD16—64no—
480SD16—184no—
481M16—32no—
482M16—61no—
483M16—92no—
484M16—181no—
485C2×C8—61no—
486C2×C8—181no—
487C4⋊C4—62no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C22⋊C4—62no—
491C22⋊C4—62no—
492C42—181no—
493C42—181no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—81no—
511C22×C3—81no—
512C22×C3—121no—
513C22×C3—121no—
514C22×C3—121no—
515C22×C3#93711yescharacteristic
516C22×C3#93811yescharacteristic
517C22×C3#93911yescharacteristic
518C22×C3#94011yescharacteristic
519C22×C3#94011yescharacteristic
520C22×C3#95311yescharacteristic
521C2×D3—41no—
522C2×D3—41no—
523C2×D3—41no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—42no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4—122no—
532C3×C4—121no—
533C3×C4—122no—
534C3×C4#93711yescharacteristic
535C3×C4#93711yescharacteristic
536C3×C4#93711yescharacteristic
537C3×C4#93811yescharacteristic
538C3×C4#93911yescharacteristic
539C3×C4#93911yescharacteristic
540C3×C4#93911yescharacteristic
541C3×C4#95311yescharacteristic
542Dic3—42no—
543Dic3—41no—
544Dic3—42no—
545Dic3—122no—
546Dic3—122no—
547Dic3—124no—
548C32#200711yescharacteristic, complemented, Sylow
549C23—21no—
550C23—61no—
551C23D3×#6711yescharacteristic
552Q8—21no—
553Q8—21no—
554Q8—61no—
555Q8—62no—
556Q8—62no—
557Q8—61no—
558Q8—121no—
559Q8—121no—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—61no—
565D4—61no—
566D4—121no—
567D4—121no—
568D4—242no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—61no—
575C2×C4—121no—
576C2×C4—121no—
577C2×C4—121no—
578C2×C4—121no—
579C2×C4—122no—
580C2×C4—182no—
581C2×C4—361no—
582C2×C4—361no—
583C2×C4#380511yescharacteristic
584C2×C4C2×#62511yescharacteristic
585C2×C4D3×#6711yescharacteristic
586C2×C4D3×#6711yescharacteristic
587C2×C4D3×#6711yescharacteristic
588C2×C4#381111yescharacteristic
589C8—62no—
590C8—182no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—82no—
601C2×C3—81no—
602C2×C3—81no—
603C2×C3—241no—
604C2×C3#520211yescharacteristic
605C2×C3#520511yescharacteristic
606C2×C3#522311yescharacteristic
607C2×C3#522311yescharacteristic
608C2×C3#524211yescharacteristic
609C2×C3#524611yescharacteristic
610D3—81no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—121no—
617C22—121no—
618C22—121no—
619C22#6397011yescharacteristic
620C22#6397611yescharacteristic
621C22#6397911yescharacteristic
622C4—41no—
623C4—122no—
624C4—121no—
625C4—122no—
626C4—362no—
627C4#6397011yescharacteristic
628C4#6397611yescharacteristic
629C4#6398011yescharacteristic
630C4#6398311yescharacteristic
631C3—21no—
632C3#7188111yescharacteristic, complemented
633C3#7211011yescharacteristic, complemented
634C2—21no—
635C2—21no—
636C2—81no—
637C2—241no—
638C2#1059166411yescharacteristic
639C2#1059168711yescharacteristic
640C2#1059172311yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
prime radicalC3×#5833C2
hypercenterC2×#41D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×#63827C2semidirect
4. C2×#63664C2semidirect
5. #10591221C2semidirect
6. C2×#63568C2semidirect
7. #10589167C2semidirect
37. C2×#951D3semidirect
74. C2×C3×Dic6D4semidirect
78. #3748D4semidirect
88. C3×#208D4semidirect
255. C2×Dic6#67semidirect
290. #208#67semidirect
548. C32#2007semidirect
632. C3#71881semidirect
633. C3#72110semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#58332
C2×C3×#9512
C2×#638272
C2×#636642
#105912212
C2×#635682
#105891672
#721103
#718813